As in same screen single machine, or as in 1 person per machine over Lan, or even a combination there of? And does it work the same way for the console versions? Thank you.

haven't verified it myself but here is the co-op info posted at the Co-Optimus web site:
https://www.co-optimus.com/game/5562/pc/warhammer-chaosbane.html

Core Features
Local Co-Op
4 Players
Online Co-Op
4 Players
Combo Co-Op (Local + Online)
Up to 4 Local or Online
LAN Play or System Link
Not Supported

Co-Op Extras
Downloadable Only
Co-Op Campaign
Co-Op Specific Content
Drop In/Drop Out

I read that too, but it doesn't specific split-screen, couch co-op or via LAN
I would love to know as well

On Steam, the store page for this game specifically states "shared/split-screen co-op." Granted, sometimes versions of the same game can differ some between GOG and Steam, but this is at least something to go on.